Snorri makes Bragi the god of poetry (Gylfaginning 26): son of Odin, famous for wisdom and eloquence and fair speech, and the husband of Idun. In Skaldskaparmal it is Bragi who tells the myths to Aegir, and in Lokasenna Loki mocks him as brave on the bench and backward in a fight. His name is the ordinary Old Norse word for a poem (bragr), which is why a poet can be called Bragi.
Modern Practice
Bragi is invoked at the start of a poem, a performance or any speech that has to carry: a cup of mead is poured and the first lines are spoken to him. Poets and songwriters keep him as the patron of the craft rather than of inspiration alone, and praise well given is the offering.